Average-Bid Auction

The purpose of this problem is to investigate a different auction format (a variant of this format is used for public procurement in Italy) for the private value case. The setting is identical to the one discussed in class. There is just one object to be auctioned off. For sake of simplicity, there are only two participants in the auction. The valuation of each of them is drawn from the interval [0, 100] with a uniform distribution. This auction is described as follows: The highest bid wins the object, only the winner pays, and the payment is equal to the average bid (that is, the the sum of the two bids divided by two.)

(a) What is the Nash equilibrium of this game?

(b) The common view was that the average-bid auction will collect less compared to, say, a first or second sealed-bid auction. Is this true? What is the expected revenue collected by the seller?